For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, which have allowed GR to remain the champion of gravitational theories against several other classes of competing theories. We pay particular attention to the role of GR and gravity in cosmology, one of the areas in which one gravity dominates and new phenomena and effects challenge the orthodoxy. We also review other areas where there are likely conflicts pointing to the need to replace or revise GR to represent correctly observations and consistent theoretical framework. Observations have long been key both to the theoretical liveliness and viability of GR. We conclude with a discussion of the likely developments over the next 100 years.

This paper describes a programme to map large-scale cosmic structures on the largest possible scales by using the Five hundred metre Aperture Spherical Telescope (FAST) to make a 21 cm (red-shifted) intensity map of the sky for the range 0.5 <z< 2.5. The goal is to map to the angular and spectral resolution of FAST a large swath of the sky by simple drift scans with a transverse set of beams. This approach would be complementary to galaxy surveys and could be completed before the Square Kilometre Array (SKA) could begin a more detailed and precise effort. The science would be to measure the large-scale structure on the size of the baryon acoustic oscillations and larger scale, and the results would be complementary to its contemporary observations and significant. The survey would be uniquely sensitive to the potential very large-scale features from inflation at the Grand Unified Theory (GUT) scale and complementary to observations of the cosmic microwave background.

With Planck cosmic microwave background observations, we established the spectral amplitude and tilt of the primordial power spectrum. Evidence of a red spectral tilt (ns = 0.96) at 8σ provides strong support for the inflationary mechanism, especially the slow roll of the effective scalar field in its nearly flat potential as the generator of scalar primordial perturbations. With the next generation of large-scale structure surveys, we expect to probe primordial physics beyond the overall shape and amplitude of the main, smooth, and slowly changing part of the inflaton potential. Using the specifications for the upcoming Euclid survey, we investigate to what extent we can constrain the inflation potential beyond its established slow-roll behaviour. We provide robust forecasts with Euclid and Planck mock data from nine fiducial power spectra that contain suppression and wiggles at different cosmological scales, using the Wiggly Whipped Inflation (WWI) framework to generate these features in the primordial spectrum. We include both Euclid cosmic shear and galaxy clustering, with a conservative cut-off for non-linear scales. Using Markov chain Monte Carlo simulations, we obtain an improvement in constraints in the WWI potential, as well an improvement for the background cosmology parameters. We find that apart from improving the constraints on the overall scale of the inflationary potential by 40–50 per cent, we can also identify oscillations in the primordial spectrum that are present within intermediate to small scales ($k\sim 0.01\!-\!0.2\, \mathrm{Mpc^{-1}}$).

The next generation of weak lensing probes can place strong constraints on cosmological parameters by measuring the mass distribution and geometry of the low-redshift Universe. We show that a future all-sky tomographic cosmic shear survey with design properties similar to Euclid can provide the statistical accuracy required to distinguish between different dark energy models. Using a fiducial cosmological model which includes cold dark matter, baryons, massive neutrinos (hot dark matter), a running primordial spectral index and possible spatial curvature as well as dark energy perturbations, we calculate Fisher matrix forecasts for different dynamical dark energy models. Using a Bayesian evidence calculation, we show how well a future weak lensing survey could do in distinguishing between a cosmological constant and dynamical dark energy.